Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations

As we know Runge-Kutta method is a one step method hence it is quite limited in terms of implementation in parallel, here we going to exploit and extend the favourable characteristic of Runge-Kutta method so that they can be implemented in parallel. In this thesis we are focusing in two types of Ru...

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Main Author:	Siri, Zailan
Format:	Thesis
Language:	English English
Published:	2004
Subjects:	Runge-Kutta formulas - Differential equations - Case studies
Online Access:	http://psasir.upm.edu.my/id/eprint/5546/1/FS_2004_22.pdf
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id	my-upm-ir.5546
record_format	uketd_dc
spelling	my-upm-ir.55462013-05-27T07:23:36Z Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations 2004 Siri, Zailan As we know Runge-Kutta method is a one step method hence it is quite limited in terms of implementation in parallel, here we going to exploit and extend the favourable characteristic of Runge-Kutta method so that they can be implemented in parallel. In this thesis we are focusing in two types of Runge-Kutta methods. The first one is the Diagonally Implicit Runge-Kutta (DIRK) method. The method used here is actually have been tailored made for the purpose of parallel machine where the subsequent functions evaluations do not depend on the previous function evaluations. The second family of Runge-Kutta method is the block Runge-Kutta both explicit and implicit. In this study, we exploit these methods so that we can implement in parallel mode. The C programming of the methods employed are run on a shared memory Sequent SE30 parallel computer. All the numerical results are given to illustrate the algorithms developed for the cases that we were tested. The numerical results show that the parallel algorithms of diagonally implicit Runge-Kutta (DIRK), block explicit Runge-Kutta (BERK) and block diagonally implicit Runge-Kutta (BDIRK) methods is better than sequential modes because the parallel execution time is smaller than sequential execution time. Runge-Kutta formulas - Differential equations - Case studies 2004 Thesis http://psasir.upm.edu.my/id/eprint/5546/ http://psasir.upm.edu.my/id/eprint/5546/1/FS_2004_22.pdf application/pdf en public masters Universiti Putra Malaysia Runge-Kutta formulas - Differential equations - Case studies Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Runge-Kutta formulas - Differential equations - Case studies
spellingShingle	Runge-Kutta formulas - Differential equations - Case studies Siri, Zailan Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations
description	As we know Runge-Kutta method is a one step method hence it is quite limited in terms of implementation in parallel, here we going to exploit and extend the favourable characteristic of Runge-Kutta method so that they can be implemented in parallel. In this thesis we are focusing in two types of Runge-Kutta methods. The first one is the Diagonally Implicit Runge-Kutta (DIRK) method. The method used here is actually have been tailored made for the purpose of parallel machine where the subsequent functions evaluations do not depend on the previous function evaluations. The second family of Runge-Kutta method is the block Runge-Kutta both explicit and implicit. In this study, we exploit these methods so that we can implement in parallel mode. The C programming of the methods employed are run on a shared memory Sequent SE30 parallel computer. All the numerical results are given to illustrate the algorithms developed for the cases that we were tested. The numerical results show that the parallel algorithms of diagonally implicit Runge-Kutta (DIRK), block explicit Runge-Kutta (BERK) and block diagonally implicit Runge-Kutta (BDIRK) methods is better than sequential modes because the parallel execution time is smaller than sequential execution time.
format	Thesis
qualification_level	Master's degree
author	Siri, Zailan
author_facet	Siri, Zailan
author_sort	Siri, Zailan
title	Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations
title_short	Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations
title_full	Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations
title_fullStr	Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations
title_full_unstemmed	Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations
title_sort	parallel execution of runge-kutta methods for solving ordinary differential equations
granting_institution	Universiti Putra Malaysia
granting_department	Science
publishDate	2004
url	http://psasir.upm.edu.my/id/eprint/5546/1/FS_2004_22.pdf
_version_	1747810448674127872

Parallel Execution of Runge-Kutta Methods for Solving Ordinary Differential Equations

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